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3 years ago

A closet is is 5 feet wide, 3 feet long, and 6 feet tall. A box with dimensions 2 ft × 3 ft × 2 ft is inside the closet.

Mathematics

1 answer:

Veseljchak [2.6K]3 years ago

5 0

Answer:

78 cm³ of space is left inside the closet.

Step-by-step explanation:

Given that,

A closet is is 5 feet wide, 3 feet long, and 6 feet tall. A box with dimensions 2 ft × 3 ft × 2 ft is inside the closet.

We need to find the space is left inside the closet around the box.

Space left = volume of the closet - volume of the box

= 5×3×6 - 2×3×2

= 90 - 12

= 78 cm³

So, 78 cm³ of space is left inside the closet.

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Marina86 [1]

I'm not sure if this is the easiest way of doing this, but it surely work.

Let the base of the triangle be AB, and let CH be the height. Just for reference, we have

$AH=2,\quad HB=6,\quad AC=x$

Moreover, let CH=y and BC=z

Now, AHC, CHB and ABC are all right triangles. If we write the pythagorean theorem for each of them, we have the following system

$\begin{cases}4+y^2=x^2\\36+y^2=z^2\\x^2+z^2=64\end{cases}$

If we solve the first two equations for y squared, we have

$y^2=x^2-4\\y^2=z^2-36$

And we can deduce

$z^2 = x^2+32$

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Step-by-step explanation:

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Find the missing measure Show all the work

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70 is the answer have a nice day

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3 years ago

What is the most precise name for a quadrilateral with the following vertices:

lozanna [386]

Answer:

The most precise name for a quadrilateral ABCD is a parallelogram

Step-by-step explanation:

we have

A(2,3) B(7,2) C(6,-1) D(1,0)

Plot the quadrilateral'

using a graphing tool

The quadrilateral ABCD in the attached figure

Verify the length of the sides

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find distance AB

A(2,3) B(7,2)

substitute

$d=\sqrt{(2-3)^{2}+(7-2)^{2}}$

$d=\sqrt{(-1)^{2}+(5)^{2}}$

$d_A_B=\sqrt{26}\ units$

step 2

Find distance BC

B(7,2) C(6,-1)

substitute

$d=\sqrt{(-1-2)^{2}+(6-7)^{2}}$

$d=\sqrt{(-3)^{2}+(-1)^{2}}$

$d_B_C=\sqrt{10}\ units$

step 3

Find distance CD

C(6,-1) D(1,0)

substitute

$d=\sqrt{(0+1)^{2}+(1-6)^{2}}$

$d=\sqrt{(1)^{2}+(-5)^{2}}$

$d_C_D=\sqrt{26}\ units$

step 4

Find distance AD

A(2,3) D(1,0)

substitute

$d=\sqrt{(0-3)^{2}+(1-2)^{2}}$

$d=\sqrt{(-3)^{2}+(-1)^{2}}$

$d_A_D=\sqrt{10}\ units$

step 5

Compare the length sides

AB=CD

BC=AD

Opposite sides are congruent

Verify the slope of the sides

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

step 1

Find slope AB

A(2,3) B(7,2)

substitute

$m=\frac{2-3}{7-2}$

$m=\frac{-1}{5}$

$m_A_B=-\frac{1}{5}$

step 2

Find slope BC

B(7,2) C(6,-1)

substitute

$m=\frac{-1-2}{6-7}$

$m=\frac{-3}{-1}$

$m_B_C=3$

step 3

Find slope CD

C(6,-1) D(1,0)

substitute

$m=\frac{0+1}{1-6}$

$m=\frac{1}{-5}$

$m_C_D=-\frac{1}{5}$

step 4

Find slope AD

A(2,3) D(1,0)

substitute

$m=\frac{0-3}{1-2}$

$m=\frac{-3}{-1}$

$m_A_D=3$

step 5

Compare the slopes

$m_A_B=m_C_D$

$m_B_C=m_A_D$

The slope of the opposite sides are equal, that means, opposite sides are parallel

The slopes of consecutive sides are not opposite reciprocal, that means, consecutive sides are not perpendicular

therefore

The most precise name for a quadrilateral ABCD is a parallelogram

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